On the mean square error of randomized averaging algorithms
Optimization and Control
2013-04-19 v3 Social and Information Networks
Systems and Control
Abstract
This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply our result to systems where few or weakly correlated interactions take place: these assumptions cover several algorithms proposed in the literature. For such systems we show that, when the network size grows, the deviation tends to zero, and the speed of this decay is not slower than the inverse of the size. Our results are based on a new approach, which is unrelated to the convergence properties of the system.
Cite
@article{arxiv.1111.4572,
title = {On the mean square error of randomized averaging algorithms},
author = {Paolo Frasca and Julien M. Hendrickx},
journal= {arXiv preprint arXiv:1111.4572},
year = {2013}
}
Comments
11 pages. to appear as a journal publication